I can't for the life of me understand why they don't explain what Batchelor's result actually is in these press releases. So here goes: in turbulence, scaling

I can't for the life of me understand why they don't explain what Batchelor's result actually is in these press releases. So here goes: in turbulence, scaling laws are a big thing. Specifically, it's extremely useful to know how the power density in a turbulent flow is distributed between small and large whirls. For the distribution of energy, we have the well-known Kolmogorov scaling law, that the power density scales with wavenumber to the power of -5/3. This holds approximately for all except the very largest whorls, down to the scale where viscosity begins to dominate, where there are no smaller whorls. This is known as the Kolmogorov scale. Due to a phenomenon called intermittency, we have strong reason to believe it is not exactly -5/3. These papers are concerned with the power spectrum of scalar mixing. Imagine dropping ink into a turbulent water flow, how does it distribute between small and large whorls? Batchelor [1] arrived at the result in 1958 that the power spectrum scales with wavenumber to the power of -1. This result has always been thought to be much more robust than the Kolmogorov scaling, since different approaches have given exactly the same answer. The papers linked here give a proof that this relationship is exact. From a quick skim, they are extremely technical in the mathematical sense, invoking measure theory and Sobolev spaces and Itô calculus. Certainly these results are very interesting. In some sense the big question is whether their approaches can transfer to solving outstanding questions about other phenomena in turbulence. [1] https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/smallscale-variation-of-convected-quantities-like-temperature-in-turbulent-fluid-part-1-general-discussion-and-the-case-of-small-conductivity/A8AEA175A906F98CDDB0F9ED146BB9FE https://www.cambridge.org/core/journals/journal-of-fluid-mec...